Accretion onto a black hole must be transonic. For a stationary,
adiabatic flow the specific energy E, specific angular momentum L
and mass accretion rate M are constant in space. The condition for
regularity of the transonic solution, F(L,E,M) = 0, reduces the number
of independent parameters to two. For a fixed pair of E(>O) and L
satisfying E_c > E >E_Barr (L), where E_c is a critical value and E_Barr is the potential barrier connected with the centrifugal force, the
regularity condition equation gives two different formal accretion
rates corresponding to different locations of the sonic point in the
flow. However, the physically acceptable global solution is unique:
it is always realized for the smaller of the two accretion rates.
For a non-rotating or slowly rotating black hole the accretion
occurs in two regimes: Bondi-type in which both the rotational and
relativistic effects are negligible in the transonic part, and disclike
in which they are dominant. Transition between the two, which is based
on a discontinuous jump in location of the sonic point, is caused by
a continuous change in the flow parameter (angular momentum, say).
The Bondi-type accretion defines a high state and the disklike a low
state, in the sense that the former always requires a higher accretion rate. When the black hole rotates very rapidly, however, the tworegime-
character of accretion no longer occurs, only the Bonditype
is possible.
For a flow characterized by the initial data L, E and M which
do not obey the regularity condition, the stationary, regular,
transonic accretion is impossible. The flow would oscillate between
the Bondi-type and disclike solutions, exhibiting a quasi-periodic
or chaotic behaviour. This could be used to explain the luminosity
variability of active galactic nuclei and Cyg X-1, thus providing
strong observational support for the existence of black holes.
